Nuprl Lemma : l_all-interface-predecessors
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀[P:E(X) ─→ ℙ]. ∀e:E. ((∀e'∈≤(X)(e).P[e']) ⇐⇒ ∀e':E(X). (e' ≤loc e ⇒ P[e']))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
l_all: (∀x∈L.P[x]),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-le_wf,
es-E-interface_wf,
all_wf,
Id_wf,
es-loc_wf,
l_member_wf,
es-interface-predecessors_wf,
set_wf,
l_all_iff,
l_all_wf2,
iff_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
event-ordering+_wf,
member-interface-predecessors,
l_member-set2,
equal_wf,
l_member-settype
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top).
\mforall{}[P:E(X) {}\mrightarrow{} \mBbbP{}]. \mforall{}e:E. ((\mforall{}e'\mmember{}\mleq{}(X)(e).P[e']) \mLeftarrow{}{}\mRightarrow{} \mforall{}e':E(X). (e' \mleq{}loc e {}\mRightarrow{} P[e']))
Date html generated:
2015_07_21-PM-03_37_16
Last ObjectModification:
2015_01_27-PM-06_31_17
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